### Related

? commutative;

97+105;

Calculate

? commutative;

x=18;

Calculate

? commutative;

7999+857+1;

Calculate

? commutative;

x=18;

Calculate

##### commutative

? commutative;

x=18;

Calculate

declare(".", commutat...

solve([(o+t*d-c).(o+t...

Calculate

T(x):=x*y^2;

Calculate

declare(".", commutat...

solve([(o+t*d-c).(o+t...

Calculate

T(x):=x*y^2;

Calculate

? commutative;

Calculate

### commutative

Run Example
```(%i1)load ("vect");
(%o1)           /usr/share/maxima/5.21.1/share/vector/vect.mac
(%i2) declare(".", commutative);
(%o2)                                done
(%i3) solve([(o+t*d-c).(o+t*d-c) = r^2],[t]);
2
(%o3)                [(d t + o - c) . (d t + o - c) = r ]
(%i4) ```
Run Example
```? commutative;

-- Declaration: commutative
If `declare(h,commutative)' is done, this tells the simplifier
that `h' is a commutative function.  E.g. `h(x,z,y)' will simplify
to `h(x, y, z)'.  This is the same as `symmetric'.

There are also some inexact matches for `commutative'.
Try `?? commutative' to see them.

(%o1)                                true
(%i2)  97+105;
(%o2)                                 202
(%i3) ```
Run Example
```load("vect");
(%o1)           /usr/share/maxima/5.21.1/share/vector/vect.mac
(%i2) declare(".", commutative);
(%o2)                                done
(%i3) x: vector([0, 0, 0], [1, 0, 0]);
(%o3)                    vector([0, 0, 0], [1, 0, 0])
(%i4) y: vector([0, 0, 0], [0, 1, 0]);
(%o4)                    vector([0, 0, 0], [0, 1, 0])
(%i5) z: vector([0, 0, 0], [0, 0, 1]);
(%o5)                    vector([0, 0, 0], [0, 0, 1])
(%i6) alpha: 90;
(%o6)                                 90
(%i7) beta: -90;
(%o7)                                - 90
(%i8) gama: 0;
(%o8)                                  0
a %pi
180
%pi
(%o10)                                ---
2
%pi
(%o11)                               - ---
2
(%o12)                                 0
(%i13) sinA: sin(alpha);
(%o13)                                 1
(%i14) sinB: sin(beta);
(%o14)                                - 1
(%i15) sinG: sin(gama);
(%o15)                                 0
(%i16) cosA: cos(alpha);
(%o16)                                 0
(%i17) cosB: cos(beta);
(%o17)                                 0
(%i18) cosG: cos(gama);
(%o18)                                 1
(%i19) Rz: matrix([cosG, -sinG, 0],[sinG, cosG, 0],[0, 0, 1]);
[ 1  0  0 ]
[         ]
(%o19)                            [ 0  1  0 ]
[         ]
[ 0  0  1 ]
(%i20) Rx: matrix([1, 0, 0],[0, cosA, -sinA],[0, sinA, cosA]);
[ 1  0   0  ]
[           ]
(%o20)                           [ 0  0  - 1 ]
[           ]
[ 0  1   0  ]
(%i21) Ry: matrix([cosB, 0, sinB],[0, 1, 0],[-sinB, 0, cosB]);
[ 0  0  - 1 ]
[           ]
(%o21)                           [ 0  1   0  ]
[           ]
[ 1  0   0  ]
(%i22) R;
(%o22)                                 R
(%i23) (R: (Rz . Rx));
[ 1  0   0  ]
[           ]
(%o23)                           [ 0  0  - 1 ]
[           ]
[ 0  1   0  ]
(%i24) (R: (Ry . R));
[ 0  - 1   0  ]
[             ]
(%o24)                          [ 0   0   - 1 ]
[             ]
[ 1   0    0  ]
(%i25) RT;
(%o25)                                RT
(%i26) (RT: transpose(R));
[  0    0   1 ]
[             ]
(%o26)                          [ - 1   0   0 ]
[             ]
[  0   - 1  0 ]
(%i27) ```

### Related Help

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